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Total Surface Area of Dodecahedron given Midsphere Radius Formula

GoTotal Surface Area of Dodecahedron Formula

GoTotal Surface Area of Dodecahedron given Volume Formula

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Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron. Check FAQs

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{2}

TSA - Total Surface Area of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Total Surface Area of Dodecahedron given Midsphere Radius Example

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Here is how the Total Surface Area of Dodecahedron given Midsphere Radius equation looks like with Values.

Here is how the Total Surface Area of Dodecahedron given Midsphere Radius equation looks like with Units.

Here is how the Total Surface Area of Dodecahedron given Midsphere Radius equation looks like.

2036.2278 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

2036.2278m² = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{2}

2036.2278 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

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Total Surface Area of Dodecahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Total Surface Area of Dodecahedron given Midsphere Radius?

FIRST Step Consider the formula

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{2}

Next Step Substitute values of Variables

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

Next Step Evaluate

∴

TSA = 2036.22775708634m²

LAST Step Rounding Answer

∴

TSA = 2036.2278m²

Total Surface Area of Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Dodecahedron

Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Dodecahedron

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius of Dodecahedron

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Dodecahedron

Go Total Surface Area of Dodecahedron

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Total Surface Area of Dodecahedron given Volume

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{2}{3}}

Go Total Surface Area of Dodecahedron given Face Diagonal

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Face}{1 + \sqrt{5}})}^{2}

Go Total Surface Area of Dodecahedron given Circumsphere Radius

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

How to Evaluate Total Surface Area of Dodecahedron given Midsphere Radius?

Total Surface Area of Dodecahedron given Midsphere Radius evaluator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2 to evaluate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using midsphere radius of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

How to evaluate Total Surface Area of Dodecahedron given Midsphere Radius using this online evaluator? To use this online evaluator for Total Surface Area of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (r_m) and hit the calculate button.

FAQs on Total Surface Area of Dodecahedron given Midsphere Radius

What is the formula to find Total Surface Area of Dodecahedron given Midsphere Radius?

The formula of Total Surface Area of Dodecahedron given Midsphere Radius is expressed as Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. Here is an example- 2036.228 = 3*sqrt(25+(10*sqrt(5)))*((4*13)/(3+sqrt(5)))^2.

How to calculate Total Surface Area of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Total Surface Area of Dodecahedron given Midsphere Radius using the formula - Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Dodecahedron?

Here are the different ways to Calculate Total Surface Area of Dodecahedron-

Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2

Can the Total Surface Area of Dodecahedron given Midsphere Radius be negative?

No, the Total Surface Area of Dodecahedron given Midsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Dodecahedron given Midsphere Radius?

Total Surface Area of Dodecahedron given Midsphere Radius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Dodecahedron given Midsphere Radius can be measured.

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